Nonparametric bioequivalence tests for statistical functionals and their e cient power functions

The population bioequivalence of two measurements is considered via diierentiable statistical functionals. This approach leads to eecient nonparame-tric bioequivalence tests given by the canonical gradient of the functional. The results are based on an asymptotic comparison of nonparametric power functions of rank tests. The bioequivalence regions are determined by implicit alternatives speciied by the functional. They only depend on the functional and their eecient tests but not on any prior information concerning parametric submo-dels. Beyond our asymptotic solution of the bioequivalence testing problem also a nonparametric nite sample size solution is discussed when the power function can exactly be computed for a family of Lehmann's alternatives. It is shown that exact semiparametric solutions can serve as asymptotically nonparametric solutions. Special attention is devoted to the Wilcoxon functional P(X < Y), the mean of cumulative hazards, and to the median functional which lead to the Wilcoxon test, the Savage test, and the median rank test, respectively.